Yes! There were a few darker skinned people in The Lord of the Rings trilogy.
Tom Bombadil for one was described as having a brown hand…
The Haradrim were also reportedly dark of skin…
“Then suddenly straight over the rim of their sheltering bank, a man fell, crashing through the slender trees, nearly on top of them. He came to rest in the fern a few feet away, face downward, green arrow-feathers sticking from his neck below a golden collar. His scarlet robes were tattered, his corslet of overlapping brazen plates was rent and hewn, his black plaits of hair braided with gold were drenched with blood. His brown hand still clutched the hilt of a broken sword.
It was Sam’s first view of a battle of Men against Men, and he did not like it much. He was glad that he could not see the dead face. He wondered what the man’s name was and where he came from; and if he was really evil of heart, or what lies or threats had led him on the long march from his home; and if he would not really rather have stayed there in peace…“
Ultimately while I’m sure there are a couple more people with darker skin in the trilogy, it’ll still be uncommon.
Now dark skin is uncommon in the trilogy not because Tolkien was racist but because his fantasy writing has a basis in European fairy / folk tales. And naturally Europeans at the time of those tales and at Tolkien’s time of writing were of light skin.
It’s unfortunate that darker skin is so uncommon in his books, but there’s nothing we can do about it. Lord of the Rings is full of pale people and that’s all there is to it.